Question: The sum of two numbers is $68$, and their difference is $30$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 68}$ ${x-y = 30}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 98 $ $ x = \dfrac{98}{2} $ ${x = 49}$ Now that you know ${x = 49}$ , plug it back into $ {x+y = 68}$ to find $y$ ${(49)}{ + y = 68}$ ${y = 19}$ You can also plug ${x = 49}$ into $ {x-y = 30}$ and get the same answer for $y$ ${(49)}{ - y = 30}$ ${y = 19}$ Therefore, the larger number is $49$, and the smaller number is $19$.